System and method for fast server consolidation

ABSTRACT

System and computer-implemented method for determining optimal combinations of elements having multiple dimensions, including determining the optimal number of destination servers for server consolidation, wherein existing servers are evaluated across multiple dimensions.

RELATED APPLICATION DATA

This application claims priority to Indian Patent Application No.1214/CHE/2011, filed Apr. 7, 2011, which is hereby incorporated byreference in its entirety.

BACKGROUND

With the increasing adoption of Service-oriented Architecture (SOA) andcloud computing technologies where Information Technology, includinginfrastructure, platforms and applications are delivered as services,there is an increasing use of the shared resource model. In such amodel, computing and IT resources are shared across multipleapplications. Accordingly, there is an increasing need for solutionsthat optimize the resource allocation. Power, cooling and real estatecosts represent a significant portion of the overall cost in operating acloud computing platform, service or datacenter. The reduction oroptimization of resources associated with such costs creates a netbenefit in total operating cost, reduces the need for expensiveinfrastructure and provides an opportunity to expand the platform. Thechallenge in consolidating such workloads is to minimize the number ofphysical servers while taking into consideration the resource needsacross multiple dimensions. In this space, the dimensions include, butare not limited to, CPU, memory, data storage, I/O, networkingbandwidth, network topology, and router utilizations—which are allsubject to change in real-time dependent upon user needs and workloads.

Server consolidation methods aim to provide an efficient usage ofcomputer server resources in order to reduce the total number of serversrequired for a particular software implementation, or a collection ofsoftware implementations. That is, server consolidation functions toaddress the problem of “server sprawl”. Server sprawl is understood inthe art to refer to multiple under-utilized servers consuming moreresources than is necessary to provide the functionality required by thesoftware packages loaded thereupon.

Server consolidation may generally be classified into three stages:centralization, physical consolidation and data and applicationintegration. Centralization involves moving servers to a commonlocation. Physical consolidation involves moving a large number ofexisting servers to a small number of high-performance servers. Storageconsolidation is also a kind of physical consolidation where disparateor related data and applications are integrated into a common databaseand common application. These classifications operate to reduce serverunder-utilization—typical levels of under-utilization in anon-consolidated environment may range from 15-20% of individualphysical server capacity being unused.

A technique for physical consolidation, which is well known in the art,is the use of server virtualization technology. Virtualization enablesmultiple existing servers to be moved to share the resources of a singlecomputer, or a dynamically selected grouping of computers. That is,software is used to divide one physical server into multiple isolatedvirtual environments or instances. Multiple methods of virtualizationare known to those skilled in the art, e.g., hardware emulation,para-virtualization, OS-level virtualization, application levelvirtualization, etc. Regardless of the particular virtualizationimplementation method, the goal is to minimize the number of physicalservers. This goal, minimizing the number of physical servers, competesdirectly with the twin goal of ensuring that sufficient resources aremade available to avoid performance degradation. Put another way,sufficient resources are required to avoid degradation in performance,wherein the sum of resource utilization for virtual machines on aphysical server (destination server) does not exceed the thresholdlimits prescribed for that particular destination server, while thenumber of destination servers is as small as possible to provide a costbenefit to the server consolidation process.

The optimization of destination servers may be viewed as a bin or vectorpacking problem. That is, items of different sizes must be packed into aminimum number of bins with a defined capacity. The basic bin packingproblem is as follows: given N objects, each with a value v_(i), i=1, .. . , N, these objects must be packed in as few bins as possible suchthat Σν_(t) of objects packed in the same bin does not exceed the bin'scapacity. The bin packing problem may be understood in the serverconsolidation context as follows: objects for server consolidation areexisting servers, object sizes are resource utilizations, bins aredestination servers, and the bin capacity is the utilization thresholdof the destination servers. Resource utilizations may include existingserver CPU, disk and memory requirements. Where multiple resources (CPU,disk, memory, etc.) are being considered, the resources form multipledimensions in the packing problem. The solutions to bin and vectorpacking problems are the same in the one-dimensional case. However, inmulti-dimensional cases, the problem is considered as a vector packingproblem.

A two-dimensional server packing problem may be formally understood asfollows: Let ρ_(c) _(i) and ρ_(d) _(i) be the CPU and disk utilizationof an existing server s_(i) (i=1, . . . n), X_(j) be a set of existingservers consolidated into a destination server s′_(j) (j=1, . . . , m),and R_(c) and R_(d) be the thresholds of CPU and disk utilizationsprescribed for the destination servers. Thus n existing servers are allconsolidated into m destination servers. The problem is then to minimizen under the constraints that Σ_(s) _(i) _(εx) _(j) ρ_(c) _(i) ≦R_(C) andΣ_(s) _(i) _(εx) _(j) ρ_(d) _(i) ≦R_(d). Note, however, that theperformance characteristics (CPU, disk, etc.) of a destination servermay be higher than that of an existing server. In such an instance, ifthe performance of a destination server is h times higher than that ofan existing server, CPU utilization _(ρ)measured on the existing serveris converted into _(ρ)/h on the destination server. Further, thevirtualization overhead increases the utilizations of servers running onvirtual machines and the threshold values for destination servers mustbe modified accordingly.

There are several methods well known in the art to solve suchmulti-dimensional vector packing problems, for example, the First FitDecreasing (FFD) algorithm. The FFD algorithm may be understood by thefollowing pseudo code.

sort existing servers to {s₁, ..., s_(n)} in descending order; m← 1; X₁← { }; for i ← 1 to n do  for j ← 1 to m do   if packable (X_(j), s_(i))then    X_(j) ←X_(j) ∪{s_(i)};    break   fi  end for;  if j = m + 1then /* if fail to pack s_(i), */   m ← m + 1; /* a new server is added*/   X_(m) ← {s_(i)} /* to have s_(i) */  fi end for

The FFD algorithm addresses the server packing problem by firstreceiving n existing servers and sorting them in descending order ofutilizations of a certain resource. After the algorithm is executed, itproduces server accommodations X_(j) (j=1, . . . , m), where m is thenumber of destination servers. The function packable (X_(j), s_(i))returns true if packing existing server s_(i) into destination servers′_(j) satisfies the constraints (i.e., the utilization of s′_(j) doesnot exceed a threshold for any resource); otherwise it returns false.FFD sequentially checks if all existing servers s₁, . . . , s_(n) can bepacked into one of m current destination servers. FFD then packs s_(i)into a destination server first found to be able to accommodate it. Ifs_(i) cannot be packed into any current destination server, the (m+1)-thdestination server is added to accommodate it. The complexity of thisFFD algorithm is O(n²) because m is almost proportional to n.

A second algorithm for vector packing known in the art is the LeastLoaded algorithm (LL). The LL algorithm may be understood by thefollowing pseudo code.

sort existing servers to {s₁, ..., s_(n)} in descending order; m←LB({s₁, ..., s_(n) }); while true do  for j ← 1 to m do   X_(j)←{ }   /*initialization */  end for;  for i←1 to n do   sort destination serversto {X₁, ..., X_(m)} in ascending order;   for j←1 to m do    if packable(X_(j), s_(i)) then      X_(j)←X_(j)∪{s_(i)};      break    fi   endfor;   if j= m + 1 then  /* If fail to pack s_(i), a new server is added*/    m ←m + 1;    break   fi  end for;  if i = n + 1 then      /* allpacked */   break  fi end while

The LL algorithm attempts to balance the load between servers byassigning incoming jobs to the least-loaded server. In server packing,an existing server with a high utilization is packed into a server withlow utilization. The function LB({s₁, . . . , s_(n)}) returns thetheoretical lower bound for the number of destination servers thataccommodate existing servers {s₁, . . . , s_(n)}. The lower bound is thesmallest integer of numbers larger than the sum of the utilizationsdivided by a threshold. The lower bound for the CPU is

${{LB}_{c} = {{\sum\limits_{i = 1}^{n}{\rho_{c_{i}}/R_{c}}}}},$while that for the disk is

${LB}_{d} = {{{\sum\limits_{i = 1}^{n}{\rho_{d_{i}}/R_{d}}}}.}$Function LB({s₁, . . . , s_(n)}) returns the larger integer of the twolower bounds.

There are two differences between LL and FFD. First, LL starts repackingafter a new destination server is added when it has failed to pack anexisting server into current m destination servers. This is aimed atbalancing the load between a newly added destination server and theothers. In contrast, FFD packs the existing server in question into anew destination server and continues to pack the remaining existingservers. LL initializes m to the lower bound to save time, even thoughwe can also start with m=1. Second, LL sorts destination servers (whichaccommodate X₁, . . . , X_(m)) in ascending order of utilizations eachtime before packing an existing server to pack it into a less-loadeddestination server. The complexity of LL is O(d·n² log n) where d is thedifference between the lower bound and the final number m of destinationservers.

The LL and FFD algorithms are limited in that only a single dimension isoptimized at a time, i.e., neither LL nor FFD optimize multipleresources in a simultaneous manner. Further, because each dimension mustfirst be considered independent of other dimensions, there is aninherent performance (time) cost to the optimization process.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional flow block diagram of an exemplary system.

FIG. 2 is a graph of exemplary fuzzy logic rule set that may beimplemented in an embodiment.

FIG. 3 is a flowchart of an exemplary embodiment of the consolidationprocess.

FIG. 4 is a graph of a performance comparison between the FFD, LL and anembodiment considering a two-dimensional vector packing problem.

FIG. 5 is a functional flow block diagram of an exemplary system.

DETAILED DESCRIPTION

There is a need in the art for a faster method of vector packing that iscapable of handling multiple dimensions in a simultaneous manner. Forexample, in the field of server consolidation in virtualizationenvironments, there is a specific need to be able to quickly determinethe optimal server allocation arrangement. However, the optimal solutionmust be determined in a short enough time period such that changingworkloads can be accommodated. Such environments may require thousandsof existing servers to be consolidated to a much smaller number ofdestination servers in real-time or in advance of actual load balancing.Thus, speed in determining server consolidation may take priority overaccuracy.

Various embodiments of the present invention will be described in detailwith reference to the drawings. Reference to various embodiments doesnot limit the scope of the invention, which is limited only by scope ofclaims attached hereto. Additionally, any examples set forth in thisspecification are not intended to be limiting and merely set forth someof the many possible embodiments. Also, it is to be understood that thephraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including”, “comprising”, or “having” and variations thereof herein ismeant to encompass the items listed thereafter and equivalents thereofas well as additional items.

The disclosed embodiments are a method of solving a vector packingproblem having multiple dimensions. Stated another way, the embodimentsdetermine optimal combinations of elements having values along multipledimensions, comprising the conversion of continuous values of eachdimension to be considered for packing into discrete values usingvarious techniques known in the field of fuzzy logic, generating asorted combination matrix of the elements to be packed (sorted by thevalues along each dimension), setting individual thresholds for thehighest distribution interval in each dimension or a common thresholdvalue for all dimension, and optimizing the matrix to determine theoptimal packing.

The vector packing problem, as applied in the server consolidationcontext, may be understood to encompass existing servers as objects forserver consolidation, resource utilizations as object sizes, destinationservers as bins, and the utilizations thresholds of the destinationservers as bin capacities. Object sizes include multiple dimensionalvalues and may be understood as existing server CPU, disk, I/O, memoryutilization and any other measurable requirement placed on an existingserver or network arrangement by an application, process, user orhardware. The methodologies utilized in the prior art require anindeterminate amount of time to arrive at the optimal packing solutionand are not suited to operating in a dynamic environment where user,hardware, and application workloads are in constant change. A solutionis therefore required which provides solutions to the described vectorpacking problem in a predictable period of time.

FIG. 1 depicts an overall view 100 of an embodiment. At Block 101 aMagnitude Classification Model (MCM) is defined. The MCM consists of apairing of a declared magnitude name (or state) with a defineddistribution interval. Magnitudes (or states) may be declared asrepresenting levels of utilization, e.g., full, large, medium, small, oras references for the defined distribution intervals, i.e., A, B, C, D,etc. The MCM is used in the consolidation process 103 to generate acombination matrix of the resource dimensions aligned along magnitudeclassifications. The distribution intervals in the MCM may be varied tochange the granularity or accuracy of the consolidation process 103.Accordingly, the number of defined distribution intervals impacts theamount of time it takes to complete the consolidation process 103. Areduced number of intervals results in faster sorting at the cost ofaccuracy. In an embodiment, the MCM is defined with uniform distributionintervals. The threshold values may be defined individually for eachdimension, or as a common value for all dimensions. Table 1 provides anexemplary MCM having uniform distribution intervals, divided into foursub-units. Note, however, that the intervals may be divided into as manyintervals as appropriate given the data set. For example, the intervalsmay be in uniform increments of 5%, 10%, 20%, or 25%.

TABLE 1 Name (Magnitude) Distribution Interval Full (F) Greater than orequal to 75%, but less than or equal to 100% Large (L) Greater than orequal to 50%, but less than 75% Medium (M) Greater than or equal to 25%,but less than 50% Small (S) Greater than or equal to 0%, but less than25%

The distribution intervals can be non-uniform. That is, definedthreshold ranges may include the intervals 0-10%, 10-15%, 15-25%, etc.Such an arrangement of distribution intervals may be desirable, forexample, where, based on historical data, it has been determined thatthere is a greater incidence of dimensional values under a particularmagnitude. Accordingly, the MCM may be fine tuned to capture morerealistic classifications and provide greater accuracy and granularityin the consolidation process 103. Table 2 provides an exemplary MCMhaving non-uniform distribution levels.

TABLE 2 Name (Magnitude) Distribution Interval A Greater than or equalto 70%, but less than or equal to 100% B Greater than or equal to 60%,but less than 70% C Greater than or equal to 50%, but less than 60% DGreater than or equal to 48%, but less than 50% E Greater than or equalto 46%, but less than 48% F Greater than or equal to 44%, but less than46% G Greater than or equal to 42%, but less than 44% H Greater than orequal to 40%, but less than 42% I Greater than or equal to 30%, but lessthan 40% J Greater than or equal to 0%, but less than 30%

In the instance of a single dimensional resource, i.e., a resourcehaving only one attribute, the MCM will produce a simple classificationof possible combinations. Referring to Table 1, the single dimensioncould only be classified as Full (F), Large (L), Medium (M) or Small(S), which may be represented as a one-dimensional array. In theinstance of multiple dimensional resources, the number of possiblecombinations form a combination matrix 102. The generation of acombination matrix 102 is dependent on the number of dimensions of theresources and the number of intervals in the MCM.

In an embodiment, the mapping of each dimensional value to a magnitudeclassification is implemented by applying principles of fuzzy logic.Referring to FIG. 2, it is understood by those skilled in the art thatfuzzy logic truth value assessments may be used to map dimensionalvalues to magnitude classifications.

In yet another embodiment, the mapping of each dimensional value to amagnitude classification may be implemented by the following exemplarypseudo code. The following code considers only a single dimensionalmapping (network utilization), but may be logically extended to includen number of dimensions.

new arrayList for i ← 0 to numberExistingServers do serverIntensityCombinationName=“”;  if (existingServer.Network = true){   if (existingServer.NetworkUtilization > NetworkThreshold( )*.9){   serverIntensityCombinationName=   serverIntensityCombinationName+“A”; }   else if(existingServer.NetworkUtilization >   NetworkThreshold( )*.8 {   serverIntensityCombinationName=    serverIntensityCombinationName+“B”}   ...   else if (existingServer.NetworkUtilization >  NetworkThreshold( )*.1 {    serverIntensityCombinationName=   serverIntensityCombinationName+“I” }  elseserverIntensityCombinationName=  serverIntensityCombinationName+“J” }end for

At Block 102, the combination matrix is generated, which is a simplematrix based on the number of combinations available in the MCM, definedabove. The dimensions of the matrix are the number of possiblecombinations, defined by the number of dimensions and number ofdistribution intervals being considered. In the server consolidationcontext, the number of dimensions is the number of resource attributesbeing considered. The number of total combinations is m^(n), where mequals the number of distribution intervals and n equals the number ofdimensions. For example, referring to Table 1, the simple case of fourdefined distribution intervals for a two-dimensional problem provides4²=16 total number of combinations. Accordingly, the dimensions of thecombination matrix are m^(n). The multi-dimensional combinations areinserted into the combination matrix in descending order, i.e., in orderof decreasing combinational magnitude as defined by the MCM. Thecombination matrix in this simple case (inserting all possiblecombinations for the purpose of explanation) is as follows:

$\quad\begin{pmatrix}{FF} & {FL} & {FM} & {FS} \\{LF} & {LL} & {LM} & {LS} \\{MF} & {ML} & {MM} & {MS} \\{SF} & {SL} & {SM} & {SS}\end{pmatrix}$

Table 3 provides examples of how the alternative combination matricesmay be sized.

TABLE 3 No. of Dimensions No. of Intervals Combination Matrix 2 2 2 × 22 3 3 × 3 2 4 4 × 4 2 10 10 × 10 3 2 2 × 2 × 2 3 3 3 × 3 × 3 3 10 10 ×10 × 10 n M m^(n)

A feasibility table provides the rule set for possible combinations.That is, the feasibility table defines the constraints on dimensionalvalue combinations under the defined MCM. Table 4 provides an exemplaryfeasibility table for the simple case described in Table 1.

TABLE 4 Combinations Name (Magnitude) Possible Result Full (F) Nocombination — possible, considered being at highest elevation, i.e., nocapacity to consolidate further. Large (L) May be combined Large (L) +Small (S) = with Small (S) Full (F) Medium (M) May be combined Medium(M) + Medium with Medium (M) (M) = Full (F) May be combined Medium (M) +Small (S) = with Small (S) Large (L) Small (S) May be combined Small(S) + Large (L) = with Large (L) Full (F) May be combined Small (S) +Medium (M) = with Medium (M) Large (L) May be combined Small (S) + Small(S) = with Small (S) Medium (M)

Referring to FIG. 3, the consolidation process 300 includes steps 301,302, 303, and 304. The inputs to the consolidation process 300 includethe populated combination matrix and the MCM rule set. In this example,referring to Table 1, Table 4 and considering only a two-dimensionalproblem, the initial combination matrix may be described as follows:

$\quad\begin{pmatrix}{FF} & {FL} & {FM} & {FS} \\{LF} & {LL} & {LM} & {LS} \\{MF} & {ML} & {MM} & {MS} \\{SF} & {SL} & {SM} & {SS}\end{pmatrix}$

At initial step 301, all combination elements consisting of the top mostmagnitude or distribution interval of the MCM are removed. Such elementsare considered as being completely full and cannot be packed anyfurther. The matrix may be resized to fit only the remaining elements.In this example, all elements consisting a dimensional value “F”, i.e.the top most magnitude of Table 1, are removed. Accordingly, theresulting matrix may be described as:

$\quad\begin{pmatrix}{LL} & {LM} & {LS} \\{ML} & {MM} & {MS} \\{SL} & {SM} & {SS}\end{pmatrix}$Each combination element removed in 301 is added to the total count ortotal packed element combination 302. In the server consolidationcontext, the total count is representative of the number of destinationservers. Accordingly, the current number of destination servers is 7.

The consolidation 303 of remaining elements is completed via aniterative process of combining the combination element(s) of the firstcell of the matrix with the combination element(s) of the last cell ofthe matrix. In this example, the first element LL is added to the lastelement SS with a packed element combination of FF, as defined in thefeasibility table, Table 4. If the packed element combination exceedsthe threshold for the highest MCM classification or distributioninterval defined in Table 1, then the first element is marked asequivalent to the highest classification and considered to be completelyfull and the next element is considered for consolidation. If, however,the packed element combination does not exceed the threshold for thehighest MCM classification or distribution level, then the next to lastadded element is added to the packed element combination. This processcontinues until all combination elements have been optimized. In thisexample, the packed element combination FF is at the highest MCMclassification under Table 1, and is marked as such and considered full.A subsequent consolidation iteration attempts to combine combinationelements LM and SM, resulting again in a packed element combination ofFF, which is full. Table 5 shows the possible iterations in thisexample.

TABLE 5 Iteration Combination Result 1 LL + SS = FF (Full) 2 LM + SM =FF (Full) 3 LS + SL = FF (Full) 4 ML + MS = FF (Full) 5 MM (remainder,combinations exhausted)The counts of 302 and 303 are aggregated to provide the total packedcombination count, i.e., total destination server count. In thisexample, the total is 12 destination servers. The following is exemplarypseudo code for the consolidation process 303.

existing servers {s₁, ..., s_(m)} having attributes {a₁, ..., a_(n)}MagnitudeCombination [ ] ← [s₁.a₁.a_(...).a_(n), s₂.a₁.a_(...).a_(n) ,..., s_(m).a₁.a_(...).a_(n)] existingServerCount ← m;destinationServerCount ← 0; for x ← 1 to m do  for y ← 1 to n do   ifs_(x).a_(n).Magnitude contains any attribute matching top MCM  Classification “A”    destinationServerCount =destinationServerCount + 1;   else    populate the MagnitudeCombination[] by increasing the count    of the respective combination end for for i← 1 to MagnitudeCombination[ ].size  if (MagnitudeCombination[k].Count != 0)   for l ← (MagnitudeCombination[MagnitudeCombination.size − k]) to   (MagnitudeCombination[ ].size)    if (MagnitudeCombination[k].Count != 0    && (MagnitudeCombination[l]) ! = 0     && MagnitudeCombination[k]not equal to     MagnitudeCombination[l]))     if(MagnitudeCombination[k].Count ≧     MagnitudeCombination [l].Count)     destinationServerCount = destinationServerCount +      MagnitudeCombination[l].Count;      MagnitudeCombination[k].Count=      MagnitudeCombination[k].Count −      MagnitudeCombination[l].Count;      MagnitudeCombination[l].Count= 0;     end if    else     destinationServerCount =destinationServerCount +      MagnitudeCombination[k].Count;    MagnitudeCombination[l].Count =     MagnitudeCombination[l].Count −     MagnitudeCombination[k].Count;      MagnitudeCombinatino[k[.Count =0;  end for end for

The performance of the instant vector packing solution providessignificant advances over the prior art. These improvements are in termsof time to completion and variable granularity, among others. The priorart evaluates each dimensional value independently of other dimensionalvalues, resulting in slow performance and unpredictable time tocompletion. The disclosed embodiments 100 consider all dimensionalvalues simultaneously and significantly outperforms the prior art,especially when considering large data sets. Referring now to FIG. 4 andTable 6, a performance comparison of the prior art and the disclosedMCM-based method is provided. All methods compared consider atwo-dimensional vector packing problem and the MCM-based methodimplements a MCM of 10-subunits having equal distribution intervals. Asis understood by those skilled in the art, the MCM-based method providespredictable increases in time to completion for increased server counts.The FFD and LL methods, in comparison, experience extreme performancedegradation, i.e., substantially increased time to completion, when theexisting server count is increased. This disparity becomes morepronounced as the number of dimensions considered is increased. Theaccuracy of the MCM-based method may be improved by increasing thenumber of distribution intervals, analyzing historical data pertainingto the how the MCM may be defined and the incidence or frequency ofparticular dimensional values, implementing non-uniform distributionintervals, or a combination thereof. It is to be further appreciated bythose skilled in the art that the benefit of the disclosed embodimentsare made apparent in highly dynamic environments where dimensionalvalues are subject to frequent change. That is, in the serverconsolidation context, as resource utilizations increase, e.g., CPU,memory, disk, I/O, network, etc., the vector packing problem may readilybe reassessed as needed to provide an optimal result.

TABLE 6 No. Destination Servers/Time (ms) No. Existing Least New MCMServers First Fit Loaded Method 5,000   2,636/227 ms  2,652/1,081 ms 2,726/159 ms 10,000   5,200/542 ms  5,337/3,424 ms  5,469/194 ms 15,000 7,628/1,107 ms  7,894/7,615 ms  8,185/343 ms 20,000 10,106/1,726 ms10,501/12,951 ms 10,952/404 ms 25,000 12,570/2,492 ms 13,116/20,422 ms13,672/431 ms 30,000  15,031/3685 ms 15,641/31,157 ms 16,385/577 ms35,000 17,597/5,282 ms 18,344/40,484 ms 19,124/637 ms 40,00019,996/7,530 ms 20,919/53,962 ms 21,835/611 ms 45,000 22,453/8,064 ms23,501/68,513 ms 24,630/656 ms 50,000 24,755/10,761 ms  25,997/87,634 ms27,289/787 ms

In an another embodiment, the consolidation process 300 may include anadditional step where the arrangement of the final packed combinationsin the combination matrix, as well as the elements removed at step 301,are stored in a database, or other suitable structure known in the art,for retrieval or further processing. The arrangement of packedcombinations referred to here are the combinations represented by thepacked combination count, or destination servers.

Referring to FIG. 5, a further embodiment 500 may include a computer 509having at least a processor 501 and memory 502, an MCM Module 503, aCombination Matrix Generation Module 504, and a Consolidation Module505. MCM Module 503 may comprise a previously defined MCM, dynamicallygenerated MCM, or an MCM input by a user or device that is conveyed viaany appropriate means as is understood in the art. Combination MatrixGeneration Module 504 may perform in accordance with the embodiments ofblock 102, discussed herein. Similarly, Consolidation Module 505 mayperform in accordance with embodiments of block 103, described herein,and may include embodiments of block 104. In yet a further embodiment,the embodiment 500 may include a network 506, as is understood to thoseskilled in the art, for communication with between devices or systems507, 508, 509. The various modules consist of computer software coderecorded on computer readable media and executed by a processor. Themodules are segregated by function in this description but need not bediscrete devices or code portions. The modules can be segregated orintegrated in any manner. Various computer devices can be used, such asServers, PCs, tablets, handheld computing devices, or variouscombinations of such devices.

Application of the embodiments is not limited to the serverconsolidation context. Instead, it may be applied to anymulti-dimensional vector packing problem as appropriate. The embodimentsdescribed herein may be implemented via any appropriate computingenvironment, as understood by those skilled in the art. Further, theembodiments, in the server consolidation context, may interface withother software, hardware or any other appropriate means for gathering,storing and retrieving resource utilization data. By non-limitingexample, the disclosed embodiments may interface with a router or othernetwork-monitoring platform or device 507 for gathering usage data fordetermining the appropriate MCM or threshold values to be used. Byfurther example, the disclosed embodiments may provide a server, networkmonitoring device, or other device 508 known in the art a serverconsolidation determination, a server consolidation plan, or thearrangement of packed combinations to a third-party, including users, acentral server, or a data center.

What is claimed is:
 1. A computer-implemented method executed by one or more computing devices for determining optimal combinations of elements having multiple dimensions, the method comprising: implementing, by at least one of the one or more computing devices, a Magnitude Classification Model (MCM) that provides a plurality of MCM magnitude classifications corresponding to a plurality of distribution intervals; assigning, by at least one of the one or more computing devices, for each of a plurality of continuous values for a plurality of dimensions, each individual continuous value to one of the plurality of MCM magnitude classifications based on which of the plurality of distribution intervals includes the individual continuous value; generating, by at least one of the one or more computing devices, a combination matrix having a plurality of elements corresponding to the plurality of MCM magnitude classifications, the elements being presented in the combination matrix in a sorted combinational order, the sorted combinational order having element values descending from a first end of the combination matrix to a second end of the combination matrix; removing, by at least one of the one or more computing devices, each element assigned to the highest MCM magnitude classification and incrementing a count of packed combinations for each element removed; resizing, by at least one of the one or more computing devices, the combination matrix to fit the remaining elements; and iteratively combining, by at least one of the one or more computing devices, the remaining elements within the combination matrix to determine the optimal combination of the remaining elements.
 2. The method of claim 1, wherein iteratively combining comprises: determining whether the distribution interval associated with a combined continuous value resulting from a combination of an individual continuous value associated with a first element from the first end of the combination matrix with an individual continuous value associated with a second element from the second end of the combination matrix corresponds to the highest MCM magnitude classification, the individual continuous value associated with the first element and the individual continuous value associated with the second element being in the same dimension; assigning the highest MCM magnitude classification to the first element based at least in part on a determination that the distribution interval associated with the combined continuous value exceeds the highest MCM magnitude classification; combining the first element with the second element based at least in part on a determination that the distribution interval associated with the combined continuous value does not exceed the highest MCM magnitude classification; and removing any elements from the combination matrix which have the highest MCM magnitude classification, and incrementing the count of packed combinations for each element removed.
 3. The method of claim 2, wherein the first element is a combined element.
 4. The method of claim 1, wherein each MCM classification represents a resource utilization level and further comprising receiving, by at least one of the one or more computing devices, resource utilization data from a network monitoring device.
 5. The method of claim 1, wherein the first end is a front end of the combination matrix and the second end is a back end of the combination matrix.
 6. The method of claim 1, further comprising transmitting, by at least one of the one or more computing devices, data representative of the optimal combination of the remaining elements to a computing device external to the one or more computing devices executing the method.
 7. At least one non-transitory computer-readable medium storing computer-readable instructions that, when executed by one or more computing devices, cause at least one of the one or more computing devices to: implement a Magnitude Classification Model (MCM) that provides a plurality of MCM magnitude classifications corresponding to a plurality of distribution intervals; assign, for each of a plurality of continuous values for a plurality of dimensions, each individual continuous value to one of the plurality of MCM magnitude classifications based on which of the plurality of distribution intervals includes the individual continuous value; generate a combination matrix having a plurality of elements corresponding to the plurality of MCM magnitude classifications, the elements being presented in the combination matrix in a sorted combinational order, the sorted combinational order having element values descending from a first end of the combination matrix to a second end of the combination matrix; remove each element assigned to the highest MCM magnitude classification and increment a count of packed combinations for each element removed; resize the combination matrix to fit the remaining elements; and iteratively combine the remaining elements within the combination matrix to determine the optimal combination of the remaining elements.
 8. The at least one non-transitory computer-readable medium of claim 7, wherein the instructions that, when executed by one or more computing devices, cause at least one of the one or more computing devices to iteratively combine the remaining elements within the combination matrix further cause at least one of the one or more computing devices to: determine whether the distribution interval associated with a combined continuous value resulting from a combination of an individual continuous value associated with a first element from the first end of the combination matrix with an individual continuous value associated with a second element from the second end of the combination matrix corresponds to the highest MCM magnitude classification, the individual continuous value associated with the first element and the individual continuous value associated with the second element being in the same dimension; assign the highest MCM magnitude classification to the first element based at least in part on a determination that the distribution interval associated with the combined continuous value exceeds the highest MCM magnitude classification; combine the first element with the second element based at least in part on a determination that the distribution interval associated with the combined continuous value does not exceed the highest MCM magnitude classification; and remove any elements from the combination matrix which have the highest MCM magnitude classification, and incrementing the count of packed combinations for each element removed.
 9. The at least one non-transitory computer-readable medium of claim 8, wherein the first element is a combined element.
 10. The at least one non-transitory computer-readable medium of claim 7, wherein each MCM classification represents a resource utilization level and further storing computer-readable instructions that, when executed by one or more computing devices, cause at least one of the one or more computing devices to receive resource utilization data from a network monitoring device.
 11. The at least one non-transitory computer-readable medium of claim 7, wherein the first end is a front end of the combination matrix and the second end is a back end of the combination matrix.
 12. The at least one non-transitory computer-readable medium of claim 7, further storing computer-readable instructions that, when executed by one or more computing devices, cause at least one of the one or more computing devices to transmit data representative of the optimal combination of the remaining elements to a computing device external to the one or more computing devices executing the instructions.
 13. A method executed by one or more computing devices for determining optimal combinations of elements having values along multiple dimensions, the method comprising: setting, by at least one of the one or more computing devices, threshold values for each dimension or common threshold values for all dimensions corresponding to a plurality of MCM magnitude classifications; converting, by at least one of the one or more computing devices, continuous values of each dimension to be considered for packing into one of the plurality of MCM magnitude classifications using fuzzy logic; generating, by at least one of the one or more computing devices, a sorted combination matrix having a plurality of elements corresponding to the plurality of MCM magnitude classifications, the elements being presented in the combination matrix in a sorted combinational order, the sorted combinational order having element values descending from a first end of the combination matrix to a second end of the combination matrix; removing, by at least one of the one or more computing devices, each element assigned to the highest MCM magnitude classification and incrementing a count of packed combinations for each element removed; resizing, by at least one of the one or more computing devices, the combination matrix to fit the remaining elements; and iteratively combining, by at least one of the one or more computing devices, the remaining elements within the combination matrix to determine the optimal combination of the remaining elements.
 14. The method of claim 13, further comprising transmitting, by at least one of the one or more computing devices, data representative of the optimal combination of the remaining elements to a computing device external to the one or more computing devices executing the instructions.
 15. An apparatus for determining optimal combinations of elements having multiple dimensions, the apparatus comprising: one or more processors; and one or more memories operatively coupled to at least one of the one or more processors and having instructions stored thereon that, when executed by at least one of the one or more processors, cause at least one of the one or more processors to: implement a Magnitude Classification Model (MCM) that provides a plurality of MCM magnitude classifications corresponding to a plurality of distribution intervals; assign, for each of a plurality of continuous values for a plurality of dimensions, each individual continuous value to one of the plurality of MCM magnitude classifications based on which of the plurality of distribution intervals includes the individual continuous value; generate a combination matrix having a plurality of elements corresponding to the plurality of MCM magnitude classifications, the elements being presented in the combination matrix in a sorted combinational order, the sorted combinational order having element values descending from a first end of the combination matrix to a second end of the combination matrix; remove each element assigned to the highest MCM magnitude classification and increment a count of packed combinations for each element removed; resize the combination matrix to fit the remaining elements; and iteratively combine the remaining elements within the combination matrix to determine the optimal combination of the remaining elements.
 16. The apparatus of claim 15, wherein the instructions that, when executed by at least one of the one or more processors, cause at least one of the one or more processors to iteratively combine the remaining elements within the combination matrix further cause at least one of the one or more processors to: determine whether the distribution interval associated with a combined continuous value resulting from a combination of an individual continuous value associated with a first element from the first end of the combination matrix with an individual continuous value associated with a second element from the second end of the combination matrix corresponds to the highest MCM magnitude classification, the individual continuous value associated with the first element and the individual continuous value associated with the second element being in the same dimension; assign the highest MCM magnitude classification to the first element based at least in part on a determination that the distribution interval associated with the combined continuous value exceeds the highest MCM magnitude classification; combine the first element with the second element based at least in part on a determination that the distribution interval associated with the combined continuous value does not exceed the highest MCM magnitude classification; and remove any elements from the combination matrix which have the highest MCM magnitude classification, and incrementing the count of packed combinations for each element removed.
 17. The apparatus of claim 16, wherein the first element is a combined element.
 18. The apparatus of claim 15, wherein each MCM classification represents a resource utilization level and wherein at least one of the one or more memories has further instructions stored thereon, that, when executed by at least one of the one or more processors, cause at least one of the one or more processors to receive resource utilization data from a network monitoring device.
 19. The apparatus of claim 15, wherein the first end is a front end of the combination matrix and the second end is a back end of the combination matrix.
 20. The apparatus of claim 15, wherein at least one of the one or more memories has further instructions stored thereon, that, when executed by at least one of the one or more processors, cause at least one of the one or more processors to transmit data representative of the optimal combination of the remaining elements to a computing device external to the apparatus. 